The "Heart" Radical on the Bottom: したごころ

Rather than using just こころ for such situations, some would call that low-lying radical したごころ (or 下心), meaning, "kanji 'heart' radical on the bottom." Others, however, reserve that term for the variant form at the bottom of characters. This alternative form looks almost like a mirror image of the radical in 思. Some examples:

添 (1631: to accompany)
慕 (1788: to adore, yearn for)

The "Heart" Radical on the Left: りっしんべん

When the "heart" radical moves to the left side of a character, it changes dramatically, losing a stroke and becoming very sharp: 忄. Known as りっしんべん (or 立心偏), this shape means "kanji 'heart' radical on the left." A few specimens:

A Heartless Character

Instead of a "heart" radical, we find the "clothing" radical (衣)! That's one materialistic inner heart!

Heartless Compounds

Now for a compound (rather than a lone character) that seems to be about hearts but is radically heartless:

肚裏 (とり: in the heart) one's mind + hidden from view

This compound refers, not to the organ pounding in the chest, but rather to feelings—specifically, ones that people have hidden (pushed to the back?), rather than expressing. Although 肚 is a non-Joyo kanji for "belly," it can also mean "one's mind, one's real intentions." And while 裏 often means "reverse side, rear," in this case it likely means "hidden from view."

Here's another term pertaining to feelings:

胸襟 (きょうきん: one's heart) feelings + heart

Typically, 胸 (840) means "chest" and 襟 (1181) is "collar," but they burst into bloom here with rich figurative meanings—namely, "feelings" and "heart."

As it turns out, the Japanese store their feelings in their chests just about as much as in their hearts. Chests are for storage, are they not?! In that spirit, it's possible to say this:

胸に納める (むねにおさめる: to keep to oneself) feelings + to store

A sample sentence:

このことは私の胸に納めておきます。
I'll keep this to myself (telling nobody).

私 (わたし: I)

Terms for the Heart

We've seen quite a few terms referring to the soulful, intangible heart, the center of deep emotions and profound reflections. That's also true of the 心 kanji when it stands alone. To write the word for the thing that thumps in your chest, pair 心 with 臓 (viscera). In other words:

Talk to a psychologist about your 心 (こころ: heart).
Talk to a cardiologist about your 心臓 (しんぞう: heart).